When you push from staging to live or live to staging, we automatically do find and replaces of URLs in the database. We don't change emails, or other items, just URLs. Sometimes our find and replace is unable to replace all of the URLS.
When that happens, you may need to use an extra plugin. Users have had good results out of the following plugins:
Velvet Blues - https://wordpress.org/plugins/velvet-blues-update-urls/ it's old, but seems to still work very well.
Go Live Update URLs - https://wordpress.org/plugins/go-live-update-urls/
Once you run this, do a full cache clear via our Tools > Quick Fix > Clear All Nginx Caches.